The thickness of glass and the longest wavelength

[Penguin98]

Homework Statement

In your research lab, a very thin, flat piece of glass with refractive index 2.00 and uniform thickness covers the opening of a chamber that holds a gas sample. The refractive indexes of the gases on either side of the glass are very close to unity. To determine the thickness of the glass, you shine coherent light of wavelength λ0 in vacuum at normal incidence onto the surface of the glass. When λ0= 496 nm, constructive interference occurs for light that is reflected at the two surfaces of the glass. You find that the next shorter wavelength in vacuum for which there is constructive interference is 386 nm.

(a) Use these measurements to calculate the thickness of the glass (h).

(b) What is the longest wavelength (lamda) in vacuum for which there is constructive interference for the reflected light?

Homework Equations

2t=m*lamda
rearrange to find t...

but really not sure what to do after this point, also not sure if this is the right equation.

 

[Charles Link]

There is a $\pi$ phase change for the reflection of the front surface, but not from the back surface. The equation for constructive interference will be $2nh+\frac{\lambda}{2}=m \lambda$, so that $2nh=(m-\frac{1}{2}) \lambda$, where $m$ is an integer. They tell you that $n=2.00$, and they give you two wavelengths $\lambda$ that have $m$ differ by 1. Let's see if you can determine $h$ from what I gave you. $\\$ Once you do that, to get the second part, it requires a careful look at the equation for constructive interference. $h$ needs to be positive, so once you get to that part, please give us what you think the smallest $m$ would be to have $h$ be positive, and then compute that $h$.